# [Cryptography] Uncorrelated sequence length, was: A TRNG review per day

Jerry Leichter leichter at lrw.com
Fri Oct 31 15:08:11 EDT 2014

```On Oct 31, 2014, at 2:31 PM, Bear <bear at sonic.net> wrote:
>>> A provably long uncorrelated sequence length is the same kind of
>>> "hard" guarantee as a one time pad -- although, like a one-time pad,
>>> it applies only to sequences shorter than that length.
>
>> I don't know what this means.  Any *specific* property - like a long
>> uncorrelated sequence length - is just a special instance of a way of
>> distinguishing the output of some algorithm from a true random
>> sequence.
>
> I am completely baffled by this comment.
>
> A provable uncorrelated sequence length of N or greater is a proof
> that it is NOT even theoretically possible to distinguish any
> generated sequence having length less than N from a true random
> sequence.  That is the opposite of being a way to distinguish a
> generated sequence from a truly random sequence.
The *test* "Has an uncorrelated sequence length of N or greater" is a special case of distinguisher from a random sequence.  Yes, if you are asking the question "Is this sequence distinguishable from a known random sequence?" you have to invert the output of the "USL > N" test, but that's a triviality.

BTW, I've responded based on the assumption that "uncorrelated sequence length" is actually a well-defined concept with a meaning based on the plain English words.  I just did what I should have done earlier:  A Google search in an attempt to find the technical definition.  The search finds exactly four instances of this exact phrase - all of them in the present discussion!  So I guess on the statement "Uncorrelated sequence length is a thing", the *correct* response is "citation needed".

-- Jerry

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